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A181208 Number of n X 4 binary matrices with no two 1's adjacent diagonally or antidiagonally. 1
16, 64, 484, 2704, 17424, 104976, 652864, 4000000, 24681024, 151782400, 934891776, 5754132736, 35428274176, 218096472064, 1342706197504, 8266039005184, 50888705511424, 313286601609216, 1928696564957184, 11873676328960000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 4 of A181212.

LINKS

Robert Israel, Table of n, a(n) for n = 1..1265 (n = 1..325 from R. H. Hardin)

Robert Israel, Maple-assisted proof of formula

FORMULA

Empirical: a(n) = 6*a(n-1) + 8*a(n-2) - 48*a(n-3) + 24*a(n-4) + 32*a(n-5) - 16*a(n-6).

Formula confirmed by Robert Israel, Dec 25 2017 (see link).

G.f.: 4*x*(4 - 8*x - 7*x^2 + 14*x^3 + 4*x^4 - 4*x^5) / ((1 - 8*x + 12*x^2 - 4*x^3)*(1 + 2*x - 4*x^2 - 4*x^3)). - Colin Barker, Mar 26 2018

MAPLE

f:= gfun:-rectoproc({a(n)=6*a(n-1)+8*a(n-2)-48*a(n-3)+24*a(n-4)+32*a(n-5)-16*a(n-6), a(1)=16, a(2)=64, a(3)=484, a(4)=2704, a(5)=17424, a(6)=104976}, a(n), remember):

map(f, [$1..20]); # Robert Israel, Dec 25 2017

PROG

(PARI) Vec(4*x*(4 - 8*x - 7*x^2 + 14*x^3 + 4*x^4 - 4*x^5) / ((1 - 8*x + 12*x^2 - 4*x^3)*(1 + 2*x - 4*x^2 - 4*x^3)) + O(x^30)) \\ Colin Barker, Mar 26 2018

CROSSREFS

Cf. A181212.

Sequence in context: A230970 A061449 A168091 * A175209 A141840 A203281

Adjacent sequences:  A181205 A181206 A181207 * A181209 A181210 A181211

KEYWORD

nonn,easy

AUTHOR

R. H. Hardin, Oct 10 2010

STATUS

approved

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Last modified April 6 15:23 EDT 2020. Contains 333276 sequences. (Running on oeis4.)